The Turbo Decoding Algorithm and its Relatives

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In 1993, a group of French researchers announced the invention of ``turbo-codes,'' a fundamentally new approach to the problem of attaining near Shannon limit performance on a variety of communications channel models. Many researchers believe that turbo codes are the most important new idea in error-correcting codes since Shannon's original paper. Professor McEliece's work under this NSF grant is motivated by the desire to provide a sound theoretical explanation for the experimentally verified iterative turbo decoding algorithm, which is the key innovation of the French group. McEliece's research has led to the discovery of a close connection between the turbo decoding algorithm and a number of other algorithms known in the cryptography, information theory, digital communications, signal processing, statistics, and artificial intelligence communities. McEliece and his co-workers have shown that all of these algorithms can be unified by a single technique which he calls the generalized distributive law, or GDL. In this work, the goal is to exploit the GDL to (a) search for a theoretical explanation of the turbo decoding algorithm, and (b) to devise new decoding algorithms in non-turbo situations.